A variable belt tensioner for an engine includes: a first damper; and a second damper connected to the first damper through a driver. The first damper, the second damper, and the driver causes a belt connected to a crankshaft pulley and a starter-generator pulley to have a first tensile strength when the engine including the crankshaft pulley starts, the first damper, the second damper, and the driver causes the belt to have a second tensile strength that is less than the first tensile strength when an electric power is generated by the starter-generator pulley, and the first damper, the second damper, and the driver causes the belt to have a third tensile strength that is less than the second tensile strength when the vehicle is accelerated by the engine.